For your purposes, I think the first questions that need to be asked are "What is your price range?" and "What is your skill level?" From the time I was old enough to shoulder it, I hunted rabbits with a multi-pump Crosman BB gun (a Pumpmaster, if I recall). Cost less than 100 dollars (probably less than 50, actually), and I only got into high powered air rifles when it finally broke. My .177 Gamo Silent Cat (99 dollars at WalMart) is still my default "stalking gun". Even with relatively low power, it flings 8 gr non-lead pellets with enough force and accuracy to take rabbits out to 30 yards, and does so with next to no report. For longer shots (usually leaning on a deck rail) I use my Hatsan 155 Vortex, also .177. Much more power, but much more weight and a bit more noise. With good shot placement, there is no need to spend any more than 100 dollars for a rabbit rifle. That being said, I am a huge fan of Hatsan's Quattro trigger.